if sin a+b=1 and sina-b=1/2 find a and b​

Answer:

A composite number is a positive integer that can be formed by multiplying two smaller positive integers. Equivalently, it is a positive integer that has at least one divisor other than 1 and itself.

Step-by-step explanation:

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Step-by-step explanation:

f(-3)=(-3)^2+4

=9+4

=13

hope it helps u dear friend

Answer:

Step-by-step explanation:

Given

f(x) = x² + 4

Now

f(- 3) = (-3)² + 4

       = 9 + 4

       = 13

hope it helps :)

Answer: b=10.

Step-by-step explanation: 5=b/2 b/2=5 2b/2=(5)(2) b=10

The rate of change of y with respect to x will be equal to 8 when there is a linear relationship between x and y.

The pace at which one quantity changes in relation to another quantity is known as the rate of change function. Simply said, the rate of change is calculated by dividing the amount of change in one item by the equal amount of change in another. The relationship defining how one quantity changes in relation to the change in another quantity is given by the rate of change formula.

The rate of change is given by the formula:

Here, the value of points are (-2.5,-30) and (-1,-18)

Now, substituting these values in the formula, we get

Rate of change=

= 8

Hence, the rate of change of the y with respect to x will be equal to 8 when there is a linear relationship between x and y.

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Answer:

-2

Step-by-step explanation:

Slope of any parallel line to the line y=-2x-7 is -2

Answer:

Step-by-step explanation:

150 students        van holds 8 students         small bus holds 14 students

with only 15 drivers you can only have 15 vehicles

       v  =  vans     b = buses      

eq 1)        v +    b    =   15            

eq 2)      8v +  14b  =  150      

            eq 1)       into          eq 2)                        the combined equations

       v = 15 - b    ---->   8v  +  14b  =  150   ---->      8(15 - b) + 14b  =  150        

       8(15 - b) + 14b  =  150        solve for b

        120 - 8b + 14b =  150        collect terms and subtract 120 from both sides

         120 -120 + (14 - 6)b  = 150 -120        

                               6b   =  30

                                 b   =   30/6

                                   b = 5

       noe find the number of vans  

             v + b = 15

             v  =  15 - b

             v  =  15 - 5

             v  =  10

Answer:

sum of anngles of triangle=180

a+b+c=180

55+70+m=180

125+m=180

m=180-125

m=55

Step-by-step explanation:

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The common ratio of the given Geometric progression is one-half.

Let a be first term and r common ratio of the Geometric progression.

The Geometric sequence is the form a,ar,ar^2, ...

Given that the sequence begins with 12, i.e a = 12

and also given that the sequence are in Geometric Progression.

By dividing the preceeding number by 2, we get the successive number

Then the Geometric sequence is 12, 12×1/2, 12×1/4, 12×1/8, 12×1/16 ...

= 12, 6, 3, 3/2, 3/4, ...

Common ratio = Second term / First term

= 6/12

=1/2

Therefore, the common ratio of the given geometric progression is one-half.

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Answer:

its a

Step-by-step explanation:

y = mx + b

Is parallel to line 5x - 2y = 6

Slope m= ?

write

5x - 6= 2y

(5/2)x - (6/2)= y

2.5x - 3 = y

Then Slope m= 2.5

equation is y= 2.5x + b

Now, find b

b= y - 2.5x

Replace point (-

Step-by-step explanation:

Since angles opposite congruent sides in a triangle are congruent, w=67.

Now, since the sum of the measures of the interior angles of a triangle is 180 degrees, x=180-67-67=46

Answer:

y = -11x - 13

Step-by-step explanation:

Step 1: Subtract 11x from both sides.

Therefore, the answer is y = -11x - 13.

The expressions are equivalent to 10a - 25 + 5b are option A, C and D.

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For illustration, 2x - 5 = 13. Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign.

Given that the expression is 10a - 25 + 5b.

For the given options, simplify each individual expression to determine the answer:

A. 5(2a−5+b)

= 10a - 25 + 5b

Equivalent

B. -2(-5a-25+5b)

= 10a + 50 - 10b

Not equivalent

C. 10×(a − 2.5 + 0.5b)

= 10a - 25 + 5b

Equivalent

D. (−2a + 5 − b)⋅(−5)

= 10a - 25 + 5b

Equivalent

E. −10⋅(−a−2.5−0.5b)

= 10a + 25 + 5b

Not equivalent

Hence, the expressions are equivalent to 10a - 25 + 5b are option A, C and D.

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If the columns of a 7x7 matrix D are linearly independent, we can say tha Equation Dx=b has a solution for each b in R. According to the Invertible Matrix Theorem, a matrix is invertible if the columns of the matrix form a linearly independent set; this would mean that the equation Dx = b has at least one solution for each b in Rn. The correct choice is A.

The correct choice is A: Equation Dx = b has a solution for each b in Rⁿ.

If the columns of a 7x7 matrix D are linearly independent, then by the Invertible Matrix Theorem, the matrix is invertible. This means that there exists a matrix D⁻¹such that DD⁻¹ = I, where I is the 7x7 identity matrix.

Now, consider the equation Dx = b. Since D is invertible, we can multiply both sides by D⁻¹to obtain D⁻¹(Dx) = D⁻¹b, which simplifies to x = D⁻¹b.

This shows that for any given b in Rⁿ, there exists a unique solution x in Rⁿ such that Dx = b. Therefore, the equation Dx = b has a solution for each b in Rⁿ.  The correct choice is A.

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Answer:

98 yd²

Step-by-step explanation:

From the diagram attached, The polygon is a square with the distance from the edge of the square to the center of the square = 7 yd.

The distance from the edge of the square to the center of the square is half of the diagonal. Therefore length of the diagonal = (7 yd * 2) = 14 yd

The diagonal and two sides of the triangle form a right angle triangle. Let the side of the triangle be a. Therefore the hypotenuse is the diagonal, using Pythagoras theorem:

a² + a² = 14²

2a² = 196

a² = 98

a = √98 = 7√2

The length of the side of the triangle = a = 7√2 yd

The area of the rectangle = length × length = 7√2 × 7√2  = 98 yd²

Answer:

Surface area = 2,160 in²

Step-by-step explanation:

Given:

Length of box = 15 in

Width of box = 30 in

Height of box = 24 in

Find:

Surface area

Computation:

Surface area = 2h[l+b]

Surface area = 2(24)[30 + 15]

Surface area = 48 x 45

Surface area = 2,160 in²

Answer:

Q (- 1, 6 )

Step-by-step explanation:

use the midpoint formula to find the coordinates of M then equate the x and y coordinates with the actual coordinates of M

P (11, - 10) and let Q = (x, y ) , then

\(\frac{11+x}{2}\) = 5 ( multiply both sides by 2 )

11 + x = 10 ( subtract 11 from both sides )

x = - 1

and

\(\frac{-10+y}{2}\) = - 2 ( multiply both sides by 2 )

- 10 + y = - 4 ( add 10 to both sides )

y = 6

coordinates of Q = (- 1, 6 )

The Perimeter of the new rectangle is 66 inches.

The perimeter of a rectangle is equal to two times the length plus two times the width of the rectangle.

Here, Najib cuts out a rectangle that has a perimeter of 50 inches and a length of 17 inches.

Therefore, we can use this information to find the width of the rectangle by using the formula for the perimeter:2(L + W) = P50 = 2(17 + W)25 = 17 + W8 = W

So the width of the original rectangle is 8 inches.

Najib cuts out another rectangle that is the same length (17 inches) and twice as wide.

This means that the new width of the rectangle is 2 x 8 = 16 inches.

Using the formula for the perimeter again, we can find the perimeter of the new rectangle:P = 2(L + W)P = 2(17 + 16)P = 66

Therefore, the perimeter of the new rectangle is 66 inches.

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Answer:

\(x=-7,x=-1,x=-0.289898,x=0.689898\)

or \(x=-7,x=-1,x=\frac{1}{5}-\frac{\sqrt{6}}{5},x=\frac{1}{5}+\frac{\sqrt{6}}{5}\)

Step-by-step explanation:

Factor by grouping

\(g(x)=5x^4+38x^3+18x^2-22x-7\\\\g(x)=5x^4+33x^3-15x^2-7x+5x^3+33x^2-15x-7\\\\g(x)=x(5x^3+33x^2-15x-7)+1(5x^3+33x^2-15x-7)\\\\g(x)=(x+1)(5x^3+33x^2-15x-7)\\\\g(x)=(x+1)(5x^3+35x^2-2x^2-14x-x-7)\\\\g(x)=(x+1)(5x^2(x+7)-2x(x+7)-1(x+7))\\\\g(x)=(x+1)(x+7)(5x^2-2x-1)\\\\0=(x+1)(x+7)(5x^2-2x-1)\\\)

We can easily see that the first two zeroes are \(x=-1\) and \(x=-7\), however, the third zero will need the help of the quadratic formula:

\(0=5x^2-2x-1\\\\x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\ \\x=\frac{-(-2)\pm\sqrt{(-2)^2-4(5)(-1)}}{2(5)}\\\\x=\frac{2\pm\sqrt{4+20}}{10}\\ \\x=\frac{2\pm\sqrt{24}}{10}\\ \\x=\frac{2\pm2\sqrt{6}}{10}\\ \\x=\frac{2}{10}\pm\frac{2\sqrt{6}}{10}\\ \\x=\frac{1}{5}\pm\frac{\sqrt{6}}{5}\\\\x_1\approx0.689898\\\\x_2\approx-0.289898\)

Therefore, the zeroes of the function are \(x=-7,x=-1,x=-0.289898,x=0.689898\)

Answer:

d + c = 12

d = 2c - 3

Step-by-step explanation:

Given that :

Total number of dogs and cats = 12

Let :

Dogs = d ; Cats = c

d + c = 12

Number of dogs = 2 times the number of cats less than 3 ;

Mathematically,

d = 2c - 3

The system of equations to model the situations are,

d + c = 12 and d = 2c - 3.

System of equations are a set of two or more equations which has to be solved together, which means the solution we get after solving these equations must be satisfying for all the equations given.

System of equations will get a unique solution if the number of variables in the equation is equal to the number of equations in the system.

Let 'c' denote the number of cats and 'd' denote the number of dogs.

Total number of dogs and cats = 12

That is, d + c = 12

Number of dogs is 3 less than twice the number of cats.

So, d = 2c - 3

Hence the system of equations to model the given statements is,

d + c = 12

d = 2c - 3

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Pick out the largest and the smallest integers from -3, -7, -42, 0, 5, 38, 11, -1, 15, -99

largest: 38

smallest: -99

Answer:

p is greater ta\han or equal to 13

Step-by-step explanation:

p + 78 is greater than 90

p has to be greater than the number plus 78 that equals 90

that would be 12

p is greater than or equal to 13

Answer:

answer on the picture. Let me know if I am right!

Answer: Book has 130 Pages, pages left 52

Step-by-step explanation:

If 3/5 = 78 pages

5/5 = 78/3 ×5/1 = 390/ 3 = 130 pages

Pages left is 130- 78 = 52 Pages

The error in finding the measure of one exterior angle of a regular polygon lies in using the formula 360°/n, where n is the number of sides of the polygon.

The formula 360°/n is used to find the measure of each exterior angle of a regular polygon. It is based on the idea that the sum of all exterior angles of any polygon is always 360 degrees. However, this formula assumes that the polygon has internal angles of 180°, which is true only for regular polygons.

The error occurs when this formula is applied to a non-regular polygon, as non-regular polygons have varying internal angles. Using the formula 360°/n for a non-regular polygon will give incorrect results because the internal angles are not all equal.

For regular polygons, each exterior angle is indeed 360°/n, and the sum of all exterior angles will be 360 degrees. However, for non-regular polygons, this formula cannot be used, and the measures of exterior angles must be calculated differently based on their internal angles and sides.

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The error in finding the measure of one exterior angle of a regular polygon is they divided 360 by 10 instead of 5.

Given that,

There are a total of 10 exterior angles, two at each vertex, so the measure of one exterior angle is 360°/10 = 36°.

Here, at each vertex there are two angles.

So, there must be 5 vertices and 5 sides.

Then, the measure of one exterior angle = 360°/5

= 72°

Therefore, the error in finding the measure of one exterior angle of a regular polygon is they divided 360 by 10 instead of 5.

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"Your question is incomplete, probably the complete question/missing part is:"

Describe and correct the error in finding the measure of one exterior angle of a regular polygon. There are a total of 10 exterior angles, two at each vertex, so the measure of one exterior angle is 360°/10 = 36°.

If P(B)=0.3, P(A|B)=0.5, P(B')=0.7and P(A|B')=0.8, then the value of the probability P(B|A)= 0.2113

To find the value of P(B|A), follow these steps:

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Answer:

d: 83

e: 97

f: 83

Step-by-step explanation:

d: We first have to find out f, so f and d can be alternate interior angles, which means they can be congruent to each other.

e: e is a vertical angle to the given angle, which means they are congruent, making it also 97 degrees.

f: f is a supplementary angle to the given angle, which means we can subtract 97 from 180 to give us 83.

Going back to angle d, now that we know f is 83 degrees, then d is an alternate interior angle, so d=f, meaning d is also 83 degrees.

Hope this helps! :)

Declan's reasoning does make sense. This is because 3/4 and 1/2 have the same denominator, and 3/4 is a larger fraction than 1/2.

Therefore, it is reasonable to assume that 3/4 is greater than 6/12 because 6/12 simplifies to 1/2. Simplifying fractions means dividing the numerator and denominator by the same number, in this case, 6 is divisible by 2, so we can reduce the fraction to 1/2.

So, Declan is correct in his reasoning that 3/4 is greater than 6/12. It is important to understand the relationship between fractions and their denominators to make such comparisons accurately.

3/4 = 9/12

1/2 = 6/12

6/12 = 6/12

Since 9/12 (which is equivalent to 3/4) is greater than 6/12 (which is equivalent to 1/2), we can say that 3/4 is indeed greater than 6/12.

Therefore, Declan's reasoning is correct.

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